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Trigonometric equations
The area rule
100

One of your classmates is solving this equation:

tanα=−0,58

Her calculator tells her that the angle is α=−30°. For the general solution, what must she add onto this angle? (Take k as an element of the integers.)

ANSWER CHOICES:

A - 0°k

B - 360°k

C - 180°k

D - None of the above 

C - 180°k

100

One of your classmates is working on a trigonometry worksheet about the area rule. The worksheet has a triangle with sides 5, 6, and 7, and one angle labelled 45°. She wrote the area rule equation below the triangle diagram. But they made a mistake and the equation is incorrect.

(show the graph Mr) 

change the 5 to 6.

200

Given the equation x=120°+360°k,k∈Z for the values of angle x, determine the value of the angle if k=1k=1.

x = 480°

200

The figure below is drawn to scale, and it shows a triangle. One angle is labelled 83°. And the sides next to that angle are 10 and 6.

(Show graph Mr.)

Determine the area of the triangle.

29,78

300

Solve the following equation. Give the general solution.

3tanβ −5=3,4

INSTRUCTION: Round your answers to one decimal place, and if there is more than one answer, separate the answers with " ; " like this:

15,4+360k;164,6+360k



β=180 k + (703/10)

300

What does it mean to find an answer "in terms of x"?

 should include x.

400

Redraw the graph of g. On the same system of axes, draw the graph of p(x)=−sinx  for the interval −90°≤x≤225°.

Clearly show all intercepts with the axes, the coordinates of the turning points, and the end points of the graph.

From your graph of p, read off and provide the coordinates asked for in the questions below. (show leaners the graph Mr.)


  1. the y-intercept of p is: (0°;0)
  2. the x-intercepts of p are: (0∘;0)
  3. the maximum turning point of p is: (−90∘;1)
  4. the minimum turning point of p is: (90∘;−1)



400

The figure below shows parallelogram KLMN. Side MN is 9 cm long, and side LM is 17 cm long, as labelled. The angle at vertex KK is labelled ψψ, and the area of the parallelogram is 42 cm2. The diagram is not drawn to scale.

(show graph) 

sinψs is 14/51

500

Find the solution for the equation below if α∈(−180°;0°]:

−3tan(3α+60°)−3=−1,2

INSTRUCTION: Round your answers to two decimal places, and if there is more than one answer, separate the answers with the " ; " symbol.

a= -150,32 ; -90,32 ; -30,32

500

The figure below shows parallelogram ABCD. Side CD is 17 m long, and side AD is 19 m long, as labelled. The angle at vertex AA is labelled ψψ, and the area of the parallelogram is 52 m2. The diagram is not drawn to scale.

show graph. 

sinψ is 52/323.